Shavers and other medical instruments for mechanical and/or electrosurgical ablation of tissue often have an integrated fluid channel for irrigating the operating site or for suctioning the ablated tissue. A valve can be provided in order to control the flow of fluid and, therefore, the irrigating or suctioning effect. Particularly if ablated tissue is sucked through the fluid channel, the medical instrument, including the fluid channel, has to undergo thorough mechanical cleaning after each use. This applies in particular to a valve, with its relatively complex surface shapes, provided in the fluid channel.